Joint Density of Bivariate Gaussian Random Variables

This Demonstration shows a 3D plot and a plot of a bivariate Gaussian (normal) density with zero means. You can drag the sliders for the standard deviations and and correlation coefficient for the random variables.

1. Start with the default variances of 1 and note the effect of changing the correlation coefficient. What are the possible angles of the major axis of the ellipses you create?

2. Now set the correlation coefficient to a value close to . Then adjust the standard deviations for the two random variables. What are the possible angles of the major axis of the ellipses you create?

3. Now set the correlation coefficient to a value close to . Then adjust the standard deviations for the two random variables. What are the possible angles of the major axis of the ellipses you create?